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Netlab Reference Manual rbfhess
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<H1> rbfhess
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<h2>
Purpose
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Evaluate the Hessian matrix for RBF network.

<p><h2>
Synopsis
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<PRE>
h = rbfhess(net, x, t)
[h, hdata] = rbfhess(net, x, t)
h = rbfhess(net, x, t, hdata)
</PRE>


<p><h2>
Description
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<CODE>h = rbfhess(net, x, t)</CODE> takes an RBF network data structure <CODE>net</CODE>,
a matrix <CODE>x</CODE> of input values, and a matrix <CODE>t</CODE> of target
values and returns the full Hessian matrix <CODE>h</CODE> corresponding to
the second derivatives of the negative log posterior distribution,
evaluated for the current weight and bias values as defined by
<CODE>net</CODE>.  Currently, the implementation only computes the
Hessian for the output layer weights.

<p><CODE>[h, hdata] = rbfhess(net, x, t)</CODE> returns both the Hessian matrix
<CODE>h</CODE> and the contribution <CODE>hdata</CODE> arising from the data dependent
term in the Hessian.

<p><CODE>h = rbfhess(net, x, t, hdata)</CODE> takes a network data structure
<CODE>net</CODE>, a matrix <CODE>x</CODE> of input values, and a matrix <CODE>t</CODE> of 
target values, together with the contribution <CODE>hdata</CODE> arising from
the data dependent term in the Hessian, and returns the full Hessian
matrix <CODE>h</CODE> corresponding to the second derivatives of the negative
log posterior distribution. This version saves computation time if
<CODE>hdata</CODE> has already been evaluated for the current weight and bias
values.

<p><h2>
Example
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For the standard regression framework with a Gaussian conditional
distribution of target values given input values, and a simple
Gaussian prior over weights, the Hessian takes the form
<PRE>

    h = beta*hdata + alpha*I
</PRE>


<p><h2>
See Also
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<CODE><a href="mlphess.htm">mlphess</a></CODE>, <CODE><a href="hesschek.htm">hesschek</a></CODE>, <CODE><a href="evidence.htm">evidence</a></CODE><hr>
<b>Pages:</b>
<a href="index.htm">Index</a>
<hr>
<p>Copyright (c) Ian T Nabney (1996-9)


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